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In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...
2021
This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which ...
Risk assessment of dam's running status is an important part of dam management. A data-driven method based on monitored displacement data has been applied in risk assessment, owing to its easy operation and real-time analysis. However, previous data-driven ...
We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called "chain" of random variables, defined by a source distribution X-(0) with high min-entropy and a number (say, t in total) of arbitrary functions (T-1,.. ...
Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...
The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the r ...
The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...
The strength of a brittle material is determined by the extreme tail of its crack-size distribution. The Weibull ansatz of algebraic distributions has been widely used but is not derived from any physical mechanism, and recent results on randomly depleted ...
